Problem 6 A company XYZ that makes radial tires of a particular size wants to in
ID: 3150319 • Letter: P
Question
Problem 6 A company XYZ that makes radial tires of a particular size wants to investigate whether the mean tread life of their tires exceed the mean tread life of a competing brand made by company ABC by more than 5,000 miles. A random sample of 45 tires by company XYZ yielded an average tread life of 42,500 miles with a standard deviation of 2200 miles. Whereas, a random sample of 45 tires made by company ABC yielded an average of 36,800 miles and a standard deviation of 1500 miles.
(a) State the hypotheses.
(b) Test the relevant hypotheses at 1% level of significance using the critical value approach. What do you conclude?
(c) To what type of error are you subject?
(d) What is the p-value of the test?
Explanation / Answer
a) H0:mutread life XYZ-mutread life ABC=0 (Difference in mean tread life of XYZ and ABC is same)
H1: mutread life XYZ-mutread life ABC>0 (Mean tread life os XYZ is greater that ABC)
b) For independent groups,
SE(xbarXYZ-xbarABC)=sqrt [s^2XYZ/nXYZ-s^2ABC/NABC]=sqrt[2200^2/45+1500^2/45]=396.93
t=(xbarXYZ-xbarABC)/SE(xbarXYZ-xbarABC)=(42500-36800)/396.93=14.36
The critical t at df=77, and alpha=0.01 is 2.38. The test statistic falls in critical region, therefore, reject null hypothesis. There is sufficient sample evidence to conclude that mean tread life of radial tyres of particular size by XYZ exceed that of ABC.
c) The null hypothesis is false but if one fails to reject it one is subject to Type II error.
d) The exact p value is 0.000.